- #1

keyzan

- 32

- 11

- Homework Statement
- determine the possible outcomes of a measurement of J^2 and Jz being J=L+S, the total angular momentum and the related probabilities.

- Relevant Equations
- -

Hi guys, I have a problem with point 2 of this exercise:

The electron of a hydrogen atom is initially found in the state:

having considered the quantum numbers n,l,m and epsilon related to the operators H, L^2, Lz and Sz.

I am asked: determine the possible outcomes of a measurement of J^2 and Jz being J=L+S, the total angular momentum and the related probabilities.

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I find the theory of total angular momentum complicated to say the least and I can't quite understand how to calculate the probabilities of the outcomes. Considering exclusively the up component to simplify the calculations (for the moment), I obtain results of J^2 and Jz:

J^2 results: 3/2, 1/2

Outcomes of Jz for j=3/2: -3/2, -1/2, 1/2, 3/2

Outcomes of Jz for j=1/2: -1/2, 1/2

Now I can't figure out how to calculate the probabilities for each outcome. Maybe I should consider that the state with the old quantum numbers splits into 6 states? I really don't know how to continue please help me.

The electron of a hydrogen atom is initially found in the state:

having considered the quantum numbers n,l,m and epsilon related to the operators H, L^2, Lz and Sz.

I am asked: determine the possible outcomes of a measurement of J^2 and Jz being J=L+S, the total angular momentum and the related probabilities.

---------------------------------------

I find the theory of total angular momentum complicated to say the least and I can't quite understand how to calculate the probabilities of the outcomes. Considering exclusively the up component to simplify the calculations (for the moment), I obtain results of J^2 and Jz:

J^2 results: 3/2, 1/2

Outcomes of Jz for j=3/2: -3/2, -1/2, 1/2, 3/2

Outcomes of Jz for j=1/2: -1/2, 1/2

Now I can't figure out how to calculate the probabilities for each outcome. Maybe I should consider that the state with the old quantum numbers splits into 6 states? I really don't know how to continue please help me.